[pedroperez80]

When my Macbook is plugged it works fine, but when I unplugged the power cord it shutsdown completly, its rare because the battery is fully charged, or at least that what the system tells me?
Also it wont startup without the power cord plugged.

Any suggestions of what might be the problem?

Black Macbook 2ghz Intel core duo, 2gb RAM, Mac OSX 10.5.1

[mduell]

Defective parts, probably the DC converter or logic board... call AppleCare.

[analogika]

Get the battery replaced:

Apple - Support - MacBook and MacBook Pro Battery Update

[nickw311]

perhaps some dead cells in the battery?

call AppleCare.

[analogika]

Might be the battery, though.